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An axisymmetric model for magnetized electrons in a Hall thruster, to be used in combination with a particle-in-cell model for heavy species, is presented. The main innovation is the admission of exchanges of electric current at the chamber walls, thus making the model applicable to a larger variety of Hall thrusters. The model is fully 2-D for regular magnetic topologies. It combines an equilibrium law for collisionless dynamics along the direction parallel to the magnetic field with drift-fluid equations for perpendicular transport. These are coupled to sheath models for the interaction with different types of walls. The derivation of a parabolic differential equation for the temperature and the full computation of the electric field work improves clarity and accuracy over previous models. Simulations of a Hall thruster with an intermediate current-driving electrode, operating in emission, floating, and collection modes are presented. Enhancement of thrust efficiency is found for the electrode working in the high-emission mode if the magnetic field strength is adjusted appropriately. The two-stage floating mode presents lower wall losses, lower plume divergence, and higher efficiency than the equivalent one-stage configuration.